$1\mathrm{.}4\mathrm{.}11$ Computing maximum thoughput. Consider the scenario shown below, with $10$ different servers $($three shown$)$ connected to $10$ different clients over ten three$-$hop paths. The pairs share a common middle hop with a transmission capacity of R $=300$ Mbps$.$ The four links from the servers to the shared link have a transmission capacity of RS $=90$ Mbps$.$ Each of the four links from the shared middle link to a client has a transmission capacity of RC $=50$ Mbps$.$

What is the end$-$end maximum throughput on one of the the$-$hop paths, assuming all servers are sending at the maximum rate possible to their clients?

Group of answer choices

$300$ Mbps

$50$ Mbps

$90$ Mbps

$440$ Mbps

$30$ Mbps